基于小波的廣義時(shí)頻分布及其與Cohen類的關(guān)系
The Generalized Time-Frequency Distribution Based on Wavelet and Its Relation with Cohens Class
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摘要: STFT, WT, WVD和Cohen類是目前信號(hào)分析和處理的有力工具。本文用WT的二次型時(shí)頻形式分析了線性時(shí)頻特性，研究了尺度圖和變化窗譜圖與Cohen類之間的關(guān)系；將尺度圖納入到Cohen類的框架，從而使WT廣義化為時(shí)頻域、時(shí)延頻偏域的雙線性時(shí)頻分布以及譜相關(guān)域的二維頻率分布；定義了尺度圖、小波模糊函數(shù)(WAF)和小波譜相關(guān)函數(shù)(WSCF)；分析了它們的物理意義。推導(dǎo)并仿真了單頻、雙頻和高斯白噪聲的WSCF，分析了各自的特性。最后通過引入一種離散小波變換的加密算法，解決了小波時(shí)頻分布的計(jì)算問題。
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關(guān)鍵詞:
- 小波;尺度圖;小波譜相關(guān);二次時(shí)頻分布;Cohen類
Abstract: STFT, WT, WVD and Cohens class are the useful tools of signal processing. This paper analyzes the bilinear TF based on WT, and the relation between the scalogram, VWS and Cohens class, Furthermore, the scalogram is classified into Cohens class, and then WT is generalized to TF domain(scalogram)，ambiguity domain(wavelet AF) and frequency/frequency delay domain(WSCF). The WSCF characteristics of mono-frequency, dual-frequency, WGN, and fractal stochastic noise are analyzed. Finally, a dense algorithm of discrete WT is introduced to the computation of generalized TF distribution based on WT. -
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